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Optimal Control of a Multiclass, Flexible Queueing System

Author

Listed:
  • Noah Gans

    (The University of Pennsylvania, Philadelphia, Pennsylvania)

  • Garrett van Ryzin

    (Columbia University, New York, New York)

Abstract

We consider a general class of queueing systems with multiple job types and a flexible service facility. The arrival times and sizes of incoming jobs are random, and correlations among the sizes of arriving job types are allowed. By choosing among a finite set of configurations, the facility can dynamically control the rates at which it serves the various job types. We define system work at any given time as the minimum time required to process all jobs currently in the backlog. This quantity is determined by solving a linear program defined by the set of processing configurations.The problem we study is how to dynamically choose configurations to minimize the time average system work. Using bounds and heuristics, we analyze a class of service policies that is provably asymptotically optimal as system utilization approaches one, as well as a policy that in numerical studies performs near-optimally in moderate traffic. Our analysis also yields a closed-form expression for the optimal, average work in heavy traffic.This general problem has a number of applications in job shop and flexible manufacturing, in service organizations, and in the management of parallel processing and distributed database systems.

Suggested Citation

  • Noah Gans & Garrett van Ryzin, 1997. "Optimal Control of a Multiclass, Flexible Queueing System," Operations Research, INFORMS, vol. 45(5), pages 677-693, October.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:5:p:677-693
    DOI: 10.1287/opre.45.5.677
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    Citations

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    Cited by:

    1. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    2. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    3. Aksin, O. Zeynep & Harker, Patrick T., 2003. "Capacity sizing in the presence of a common shared resource: Dimensioning an inbound call center," European Journal of Operational Research, Elsevier, vol. 147(3), pages 464-483, June.
    4. Lisa Fleischer & Jay Sethuraman, 2005. "Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 916-938, November.
    5. Noah Gans & Garrett van Ryzin, 1999. "Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights," Operations Research, INFORMS, vol. 47(5), pages 675-692, October.
    6. Omar Besbes & Costis Maglaras, 2012. "Dynamic Pricing with Financial Milestones: Feedback-Form Policies," Management Science, INFORMS, vol. 58(9), pages 1715-1731, September.
    7. Mihalis G. Markakis & Eytan Modiano & John N. Tsitsiklis, 2018. "Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 460-493, May.
    8. Yuanguang Zhong & Zhichao Zheng & Mabel C. Chou & Chung-Piaw Teo, 2018. "Resource Pooling and Allocation Policies to Deliver Differentiated Service," Management Science, INFORMS, vol. 64(4), pages 1555-1573, April.
    9. Kimberly M. Wasserman & Tava Lennon Olsen, 2001. "On Mutually Interfering Parallel Servers Subject to External Disturbances," Operations Research, INFORMS, vol. 49(5), pages 700-709, October.
    10. J. G. Dai & Wuqin Lin, 2005. "Maximum Pressure Policies in Stochastic Processing Networks," Operations Research, INFORMS, vol. 53(2), pages 197-218, April.
    11. Daniel Adelman & George L. Nemhauser, 1999. "Price-Directed Control of Remnant Inventory Systems," Operations Research, INFORMS, vol. 47(6), pages 889-898, December.

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